Simplex Method Calculator : 3 Variables
Simplex method calculator for 3 variable linear programming problems. Solve LP problems with x1, x2, and x3 easily.
Simplex Calculator
How Simplex Method Calculator Works
Enter the LP Problem
Type the objective function coefficients and every constraint row with its right-hand-side value.
Choose Maximize or Minimize
Pick your optimization goal. The tool builds the initial tableau with slack variables automatically.
Run the Pivot Iterations
The calculator identifies pivot column by Cj-Zj, computes ratios, performs elementary row operations until optimal.
Read the Optimal Solution
Final tableau displays optimal variable values, Zj row, and the maximum/minimum objective value.
Sample Simplex Tableau Output
Example tableau iteration for a 2-variable maximization problem
| Basis | x1 | x2 | s1 | s2 | RHS | Cj-Zj |
|---|---|---|---|---|---|---|
| x1 | 14 | 0 | 0 | 1 | 14 | 0 |
| x2 | 7 | 1 | 0 | 0 | 7 | 5 |
| Zj | 35 | 5 | 0 | 0 | 35 |
Three-Variable Problems
With three decision variables (x₁, x₂, x₃) a problem can no longer be graphed in two dimensions, so the simplex method becomes essential. This calculator builds the tableau for three variables and any number of constraints, performing each pivot until the optimal solution is found.
How to Enter It
Write the objective as, for example, 3x₁ + 5x₂ + 4x₃ and add one constraint per line. The calculator reports the optimal objective value together with x₁, x₂, and x₃.
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Frequently Asked Questions
How does the simplex method handle 3 variables?
For 3 variables, the simplex method uses a tableau with 3 decision columns (x1, x2, x3) plus slack variables. The pivot operations proceed exactly as in 2 variables, iterating until the optimal solution is found.
Can I graph 3 variable simplex problems?
Graphing 3 variables requires a 3D plot which can be visually complex. The simplex calculator bypasses the need for graphical methods by computing the exact algebraic iterations.
Why can't I graph a three-variable problem?
A three-variable problem needs three dimensions, so it cannot be drawn on a two-dimensional graph; the simplex method solves it algebraically.
How do I write a three-variable objective?
Use the form 3x1 + 5x2 + 4x3, with one constraint per line.
Does it report all three variable values?
Yes, the calculator returns the optimal objective value together with x1, x2, and x3.